Can you give me just a hint to calculate the following limit? $$\lim_{n\to\infty}\frac{1}{(\ln n)^{\ln n}}$$ I am trying using the squeeze rule without success. I tried also l'Hopital but the limit become tougher.
Thank you.
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$\ln(n) \rightarrow \infty$ as $n \rightarrow \infty$. So, $\ln(n)^{\ln(n)} \rightarrow \infty$ as $n \rightarrow \infty$. Hence the limit is $0$.
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$\begingroup$ Please, write $\ln$ by typing
\lninstead of $ln$ made by typingln. $\endgroup$ – user93957 Jan 26 '14 at 19:06 -
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$\begingroup$ You're welcome! ;-) $\endgroup$ – user93957 Jan 26 '14 at 19:08
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2$\begingroup$ @Charlie $\infty^\infty$ is not an indeterminate form. $\endgroup$ – user93957 Jan 26 '14 at 19:14
->, write $\to$ by typing\toor\rightarrow. $\endgroup$ – user93957 Jan 26 '14 at 19:04